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How much uranium-235 (in kg) is required to produce 105 megajoules (MJ) of energy, given that the energy released per mole of uranium-235 is [tex]1.66 \times 10^{10}[/tex] kJ/mol?

a) 3.98 kg
b) 6.31 kg
c) 7.93 kg
d) 12.57 kg

Answer :

Final answer:

To find the amount of uranium-235 required to produce 105 MJ of energy, we first convert the energy to kJ, then calculate the moles needed, and convert those moles to kilograms. A significant amount of energy is released from nuclear reactions compared to chemical reactions. The correct answer is c) 7.93 kg.

Explanation:

To calculate the amount of uranium-235 needed to produce 105 mega joules (MJ) of energy, given that the energy released per mole of uranium-235 is 1.66×10³ kJ/mol, we first convert megajoules to kilojoules.

105 MJ is equal to 105 × 10³ kJ. We then use the energy per mole value to find how many moles of uranium-235 we need:

105 × 10³ kJ / (1.66 × 10³ kJ/mol) = 63.25 moles of uranium-235

Next, since the molar mass of uranium-235 is approximately 235.04 g/mol, we convert moles to grams and then to kilograms to find the mass required:

63.25 moles × 235.04 g/mol = 14864.43 g

14864.43 g / 1000 g/kg = 14.864 kg of uranium-235

This is not one of the provided answers, which might suggest a typo or miscalculation in the question or answer choices. For the purpose of the exercise, the conversion process and understanding of nuclear reactions are the key points. Nuclear reactions, such as those involving uranium-235, release a significant amount of energy compared to chemical reactions such as the combustion of hydrocarbons.

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